Description
Apply endpoint orientation to a supplied ascending-order integral.
Integration depends on the domain, orientation, coordinate change and endpoint behavior. A boundary contribution, Jacobian factor or power-tail test is a local part of an integral calculation; convergence, a valid change of variables and the complete integral require their own hypotheses.
Apply endpoint orientation to a supplied ascending-order integral.
When to use this tool
Use Integral Subinterval Orientation when evaluating the stated integral contribution, orientation, Jacobian or convergence condition.
How to use the tool and how it works
- Enter lower, upper, suppliedIntegralInAscendingOrder. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read orientedIntegral, orientation. Use the output convention below.
Apply endpoint orientation to a supplied ascending-order integral. Return zero for equal endpoints, otherwise suppliedIntegralInAscendingOrder times +1 for increasing endpoints or -1 for decreasing; orientation is sign(upper-lower).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| suppliedIntegralInAscendingOrder | Supplied Integral In Ascending Order | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| orientedIntegral | Oriented Integral | Required. Finite number. |
| orientation | Orientation | Required. Safe integer. |
{
"input": {
"lower": 3,
"upper": 1,
"suppliedIntegralInAscendingOrder": 5
},
"output": {
"orientedIntegral": -5,
"orientation": -1
}
}Limitations and assumptions
- The integral value is supplied, not evaluated; sign of the integrand and correctness of that ascending integral are not established.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Specify and analyze the complete integrand and domain, including endpoint singularities, coordinate invertibility and any omitted boundary or interior terms.
References
Similar or alternative tools
- Integral Orientation Composition Sign
Compose supplied orientation signs.
- Integral Moving Bound Normal Sign
Return moving-integral endpoint contributions.